My view is that there isn't a clear answer to this question and it may be influenced by the ownership of the playing fields or village hall. Incorporation has the advantage of creating a legal person, independently of the individuals involved. It will continue in existence provided there are still members, who normally guarantee a nominal sum.
Incorporation does not guarantee that the organisation will continue to operate effectively, that depends on willing volunteers. The drawbacks to incorporation are that it involves some extra administration and, if not all the people involved are members of the company, it creates a two tier structure.
There is the question of liability, which can be limited by incorporation. However, the scale of operation is probably not much different from that of a private home, and householders do not normally incorporate themselves! It should be possible to cover all likely liabilities through insurance. Keeping insurance in force is essential.
If incorporation is not used, then the assets can be vested in the public trustee, which obviates problems caused by all trustees becoming unavailable through ill health or death, which can easily happen if nobody is keeping an eye on the legal background.
There are advantages to having the parish council as the ultimate owner, because of the mechanisms that ensure the council's existence in perpetuity. But that may not be a popular solution if the groups are operating successfully and would feel council involvement to be an intrusion.
